SOLUTION: At the beginning of 2000 Arturo's house was worth 244 thousand dollars and Zach's house was worth 124 thousand dollars. At the beginning of 2003, Arturo's house was worth 190 thous

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Question 1124887: At the beginning of 2000 Arturo's house was worth 244 thousand dollars and Zach's house was worth 124 thousand dollars. At the beginning of 2003, Arturo's house was worth 190 thousand dollars and Zach's house was worth 158 thousand dollars. Assume that the values of both houses vary at an exponential rate.
a. Write a function f that determines the value of Arturo's house (in thousands of dollars) in terms of the number of years t since the beginning of 2000.
b. Write a function g that determines the value of Zach's house (in thousands of dollars) in terms of the number of years t since the beginning of 2000.
c. How many years after the beginning of 2000 will Arturo's and Zach's house have the same value?
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Since 2000:
(a)


Take the log of both sides




———————
The equation for Arturo’s house is:

———————————————
(b)


Take the log of both sides



—————-
The equation for Zack’s house is:

————————————-
(c)
Set equations equal



Take log of both sides


After 4 yrs
————————————-
Check:
Arturo:


Zack:



Close- error may be rounding off or
my calculating. I think method is OK



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